AnomalousNet: A Hybrid Approach with Attention U-Nets and Change Point Detection for Accurate Characterization of Anomalous Diffusion in Video Data

TL;DR

AnomalousNet addresses the challenge of accurately characterizing anomalous diffusion parameters and detecting state transitions from short, noisy video data. It combines particle tracking, an Attention U-Net that infers framewise $\alpha$, $K_{\alpha}$, and diffusion state, and a change-point detector with prediction normalization to produce coherent, piecewise diffusion profiles. The approach achieves top submissions on the 2nd AnDi Challenge for video-based tasks and demonstrates robustness across raw trajectories and video data, while highlighting CP-detection as a key area for further improvement. The framework offers a modular, scalable pathway for analyzing complex diffusion dynamics in heterogeneous environments with practical applications in biology and materials science.

Abstract

Anomalous diffusion occurs in a wide range of systems, including protein transport within cells, animal movement in complex habitats, pollutant dispersion in groundwater, and nanoparticle motion in synthetic materials. Accurately estimating the anomalous diffusion exponent and the diffusion coefficient from the particle trajectories is essential to distinguish between sub-diffusive, super-diffusive, or normal diffusion regimes. These estimates provide a deeper insight into the underlying dynamics of the system, facilitating the identification of particle behaviors and the detection of changes in diffusion states. However, analyzing short and noisy video data, which often yield incomplete and heterogeneous trajectories, poses a significant challenge for traditional statistical approaches. We introduce a data-driven method that integrates particle tracking, an attention U-Net architecture, and a change-point detection algorithm to address these issues. This approach not only infers the anomalous diffusion parameters with high accuracy but also identifies temporal transitions between different states, even in the presence of noise and limited temporal resolution. Our methodology demonstrated strong performance in the 2nd Anomalous Diffusion (AnDi) Challenge benchmark within the top submissions for video tasks.

Figures (9)

• Figure 1: Diagram of the AnomalousNet Architecture
• Figure 2: Density Distribution of Alpha and $K$ Values in the Generated Data
• Figure 3: Attention U-Net Architecture Diagram for $\alpha$ Prediction.
• Figure 4: Histogram of the anomalous diffusion exponent $\alpha$ across different models in the inference validation dataset across different physical models. The line represents the MAE of the predictions for each value of $\alpha$.
• Figure 5: Histogram of the anomalous diffusion coefficient $K$ across different models in the inference validation dataset across different physical models. The line represents the MSLE of the predictions for each value of $K$.